Question

According to CTIA, 25% of all U.S. households are wireless-only households (no landline). In a random sample of 20 households, what is the probability that

a) Exactly 5 are wireless-only?
b) Fewer than 3 are wireless-only?
c) At least 3 are wireless-only?
d) The number of wireless-only households is between 5 and 7, inclusive.

Answer 1

To find the probabilities, we will use the binomial probability formula. We can calculate the probabilities for each scenario.

Step-by-step explanation:

To find the probability for each scenario, we will use the binomial probability formula. The formula for the probability of exactly k successes in n trials is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n is the number of trials (in this case, 20 households)

k is the number of successes (the desired number of wireless-only households)

p is the probability of success (0.25, as given by CTIA)

We can now calculate the probabilities for each scenario:

a) P(X=5) = (20 choose 5) * (0.25)^5 * (0.75)^15

b) P(X<3) = P(X=0) + P(X=1) + P(X=2)

c) P(X>=3) = 1 - P(X<3)

d) P(5<=X<=7) = P(X=5) + P(X=6) + P(X=7)